**COMP-598: Quantum Information Theory**

**Time:** Tuesday and Thursday from 10:00 to 11:30 (Winter
2013)

**Room:** McConnell 103

** **

**Instructor:** Patrick Hayden

Office: ENGMC 108N

Phone: 398-5491

Email: patrick@cs.mcgill.ca

Office hours: Wednesday 10:00-12:00

**Course
description:**

This course will present the quantum
analog of Shannon s information theory. This area has seen an explosion of
interest and a correspondingly rapid technical advance over the past ten years,
largely in response to the development of quantum-mechanically based
cryptographic protocols and Shor s famous algorithm
for factoring integers. The unavoidable presence of noise in any
quantum-mechanical information processing device means
that error-correction techniques will play a crucial role in any practical
application of quantum cryptography or computing. This course will focus on
asymptotic protocols for compression, communication, error correction and state
distillation, identifying the absolute limits placed on those tasks by quantum
mechanics.

Familiarity with quantum mechanics
is recommended. The course content is very mathematical, but elementary.
Students should be comfortable with basic probability theory, linear algebra
and real analysis. The material will be covered through a combination of
lectures and student presentations.

**Course
outline:**

- Classical
information theory:
- Compression:
Shannon s noiseless coding theorem
- Error correction:
Shannon s noisy coding theorem
- The birth of the qubit: Schumacher compression
- Tools for quantum
information:
- Review of
quantum-mechanical formalism (including Bell s theorem)
- Inequalities for
von Neumann entropy
- Strong subadditivity
- Three brilliant
trivialities:
- Superdense coding
- Teleportation
- Coherent classical
communication
- The family of
quantum protocols
- The mother, father
and fully quantum Slepian-Wolf protocols
- Consequences
- Entanglement
distillation
- State merging
- Entanglement-assisted
and quantum capacities
- Quantum reverse
Shannon theorem
- The HSW theorem:
classical data through a noisy quantum channel
- A noiseless
postlude:
- Superdense coding of quantum
states and its consequences
- Majorization and entanglement
manipulation

**Grading:** 60% assignments, 40% project.

**Text:** There is no formal text for the course. However,
roughly the first month s worth of material can be found in *Quantum Computation and Quantum Information*
by Nielsen and Chuang, which is an excellent introduction to the field as a
whole. Mark Wilde s free quantum
information theory book is excellent and provides a different perspective
on much of the material. *Elements of
Information Theory* by Cover and Thomas should meet your classical
information theory needs.

**Projects:** More information can be found here.

**Embarrassing obligatory inclusion: **

By the
direction of Senate (January 29, 2003), all course outlines have to include the
following statement:

McGill University values academic
integrity. Therefore, all students must understand the meaning and consequences
of cheating, plagiarism and other academic offences under the Code of Student
Conduct and Disciplinary Procedures (see www.mcgill.ca/integrity for more
information).